# Is $g = \{ (1,1),(2,3),(3,5),(4,7)\} $ is a function? If this is described by a formula$g(x) = \alpha x + \beta $, then what values should be assigned to $\alpha $ and$\beta $?

Last updated date: 21st Mar 2023

•

Total views: 307.5k

•

Views today: 4.86k

Answer

Verified

307.5k+ views

Hint: Here we solve the problem by finding the given set is a function or not.

Given $g = \{ (1,1),(2,3),(3,5),(4,7)\} $

Here, if we observe in the given set each element of domain has unique image so from this we can say the g is function.

Here the function g is described by a formula $g(x) = \alpha x + \beta $

Now let us substitute $x = 1$ in the formula $g(x) = \alpha x + \beta $

$\

g(1) = \alpha (1) + \beta \\

g(1) = \alpha + \beta \to 1 \\

\ $

We know that $g(1) = 1$ from the given function g

So we write the equation as

$\alpha + \beta = 1 \to 1$

Now again let us substitute $x = 2$in the formula $g(x) = \alpha x + \beta $

$\

g(2) = \alpha (2) + \beta \\

g(2) = 2\alpha + \beta \\

\ $

And we know that $g(2) = 3$from the given function g

So we can write the equation as

$2\alpha + \beta = 3$$ \to 2$

Now let us solve equation 1 and 2

We get $\alpha = 2$ and $\beta = 1$

Now we can write the formula as $g(x) = 2x - 1$

$\therefore g(x) = 2x - 1$

NOTE: We have used the domain values of g function to get the formula of g(x).

Given $g = \{ (1,1),(2,3),(3,5),(4,7)\} $

Here, if we observe in the given set each element of domain has unique image so from this we can say the g is function.

Here the function g is described by a formula $g(x) = \alpha x + \beta $

Now let us substitute $x = 1$ in the formula $g(x) = \alpha x + \beta $

$\

g(1) = \alpha (1) + \beta \\

g(1) = \alpha + \beta \to 1 \\

\ $

We know that $g(1) = 1$ from the given function g

So we write the equation as

$\alpha + \beta = 1 \to 1$

Now again let us substitute $x = 2$in the formula $g(x) = \alpha x + \beta $

$\

g(2) = \alpha (2) + \beta \\

g(2) = 2\alpha + \beta \\

\ $

And we know that $g(2) = 3$from the given function g

So we can write the equation as

$2\alpha + \beta = 3$$ \to 2$

Now let us solve equation 1 and 2

We get $\alpha = 2$ and $\beta = 1$

Now we can write the formula as $g(x) = 2x - 1$

$\therefore g(x) = 2x - 1$

NOTE: We have used the domain values of g function to get the formula of g(x).

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE